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From: Thomas on 5 Apr 2010 14:49
Hey everyone

I would like to hear if anyone could help me solving the problem below by using the PDE toolbox in matlab?

I really do hope anyone can help me...?? Thank you so much in advance...

Kind regards

Thomas


___________________Problem_________________________

I am searching for at solution function F(P,K).

The elliptic PDE is given by:

0.5*s^2*P^2*F_{PP} + 0.5*w^2*I*K*F_{KK} + a*P*F_{P} - I * F_{K} + r*F - I = 0

where F_{x} is the first order derivative wrt x, F_{xx} is the second order derivative wrt x. Furthermore V(P) is a known function.

Three boundary conditions:

F(P, 0) = V(P) %terminal condition

F(0, K) = 0 %lower boundary condition

F(P, K) = V(P)*exp(-r * K/I) - int_0^{K/I} ( I * exp{-r*t} ) dt for
P---> infinity %upper boundary condition

Free Boundary: P=P*

F(P*,K) = V(P*) %Value matching

F_{P}(P*, K) = 0 %Smooth pasting

F_{K}(P*, K) = 0 %Smooth pasting

Parameters/constants: s, w, a, r, I
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